Variable importance is a key statistical issue in exposure mixtures, as it allows a ranking of exposures as potential targets for intervention, and helps to identify bad actors within a mixture. In settings where mixtures have many constituents or high between-constituent correlations, estimators of importance can be subject to bias or high variance. Current approaches to assessing variable importance have major limitations, including reliance on overly strong or incorrect constraints or assumptions, excessive model extrapolation, or poor interpretability, especially regarding practical significance. We sought to overcome these limitations by applying an established doubly-robust, machine learning-based approach to estimating variable importance in a mixtures context. This method reduces model extrapolation, appropriately controls confounding, and provides both interpretability and model flexibility. We illustrate its use with an evaluation of the relationship between telomere length, a measure of biologic aging, and exposure to a mixture of polychlorinated biphenyls (PCBs), dioxins, and furans among 979 US adults from the National Health and Nutrition Examination Survey (NHANES). In contrast with standard approaches for mixtures, our approach selected PCB 180 and PCB 194 as important contributors to telomere length. We hypothesize that this difference could be due to residual confounding in standard methods that rely on variable selection. Further empirical evaluation of this method is needed, but it is a promising tool in the search for bad actors within a mixture.